Debt and Consumption in The United Kingdom After The Crisis

Transcription

1 Debt and Consumption in The United Kingdom After The Crisis Agnes Kovacs, May Rostom, Phil Bunn Preliminary - Do not circulate without authors permission: 4 Sept 2016 Abstract This paper investigates the relationship between mortgage leverage and consumption growth around the 2008 financial crisis. Using data from the UK s Family Expenditure Survey (FES), we first show that more indebted households made larger cuts to consumption following the financial crisis, and that this was largely driven by younger households. Second, using a life-cycle framework, we investigate the channels by which highly indebted households may have reduced consumption by more than other groups. Our key finding is that our empirical observation is most likely driven by income shocks at 2008 as well as the increased uncertainty around labor income after 2008, the effect of which varies depending on the size of household leverage. Keywords: life-cycle models, consumption, household leverage, debt, financial crisis JEL classification: D10; D11; D14; E21 Kovacs: University of Oxford; Rostom: University College London and Bank of England; Bunn: Bank of England. The authors would like to thank Orazio Attanasio, Richard Blundell, Antonio Guarino and Lars Nesheim for helpful comments and advice on this paper. Any views expressed are solely those of the author(s) and so cannot be taken to represent those of the Bank of England or to state Bank of England policy. This paper does not necessarily represent the views of the Bank of England or members of the Monetary Policy Committee or Financial Policy Committee. All errors are our own. 1

2 1 Introduction The 2008/2009 financial crisis in the UK has been characterized by a large drop in household consumption 1 and mortgage takeout at the same time. In this paper we focus on understanding how mortgage status affects households consumption behavior in the recent crisis. Using household-level data from the UK s Family Expenditure Survey (FES), we first show in our empirical model that households with a mortgage cut their consumption by more than households with no mortgage. In aggregate, we calculate that almost half of the fall in household consumption in 2009/10 was due to households who had a mortgage. Moreover, the higher the household s mortgage to income ratio (leverage) going into the crisis, the more they cut consumption afterward. In summary, households with higher levels of leverage contributed to the weakness in consumption growth more than households with lower levels of leverage. Having documented these empirical observations, we then simulate a life-cycle model with a realistic mortgage market in order to get a better understanding of the different mechanisms that drive indebted households to cut their consumption by more than other households after the 2008 crisis. Following Alan, Crossley, and Low (2012) we consider four definitions of what recession may have meant for households: a fall in the level of income, rising uncertainty around future income, a reduction in the supply of credit and a decline in house prices. The first channel works through a negative shock to income. When households face a fall in their income level, they cut back their consumption. But the size of the cutback would differ across households depending, among other things, on where they are in their life-cycle. Young households, for example, have typically had bigger falls in their income during the Great Recession than older households (they were more likely to be made unemployed). They also tend to have higher levels of secured debt than middle-aged households. If they are in a commitment contract to continue making mortgage payments, one may observe a bigger cut in consumption for these highly indebted households, as they substitute away from consumption towards meeting their mortgage obligations. The second channel plays a role when the recession is associated with higher uncertainty around future income. As uncertainty increases, households increase their precautionary savings, hence consuming less. Again, depending on where the households are at their life-cycle and consequently what their leverage is they could behave quantitatively very differently. 1 Throughout the paper, we use the term household consumption for households non-housing consumption 2

3 The third channel works through an exogenous reduction in the supply of credit. Since the crisis, banks decreased the acceptable leverages significantly, which made it increasingly difficult for households to finance consumption from topping up mortgages. This change may affect highly indebted households the most, since they are not able to withdraw additional equity from their housing at all 2. Therefore, their consumption may fall by much more than other households. The final channel we consider is a fall in house prices, which is very similar to the credit supply channel. As house prices fall, mortgagors face a reduction in their housing wealth, which increases their loan-to-value (LTV) ratios. This rise in leverage would lead to a decline in consumption in two different ways. First, in the event that the household needs to refinance (e.g. because they are moving house), they would be faced with much higher mortgage payments. To keep up with these higher payments, they would have to reduce their consumption. Second, heavily leveraged households would be unable to withdraw additional equity from their house that they would have used to maintain a certain level of consumption. As a result, heavily leveraged households may have to decrease their consumption by more than other households. Our focus is on how the differences in consumption cuts between high and lowleveraged households can be explained with the mechanisms detailed above. Using simulations we show that the observed pattern of consumption drops in the recent recession is best explained by a model in which the recession is associated either with a permanent income shock or an income uncertainty shock. Models with recessions led by a fall in credit supply or a fall in house prices do not predict differences in consumption behavior between high and low-leveraged households. The literature only has a limited number of papers analyzing the relationship between mortgages and consumption behavior. Dynan (2012) uses household level data to show that households with high leverages have experienced larger declines in spending between 2007 and 2009, after controlling for wealth effects and other factors. Mian, Rao, and Sufi (2013) show that the decline in US consumption following the crisis was greater in counties with higher leverage prior to the crisis. Baker (2013) finds that spending by highly indebted households has been more sensitive to income fluctuations and that is likely to have increased the depth of the recent recession. In the empirical sections we give detailed empirical evidence for the relationship between mortgage status and the consumption reaction of households to the 2008 crisis. More specifically we show that households with higher debt experience a much bigger drop in their consumption over the period of the crisis. This is the feature of the data which we would like to understand better. In our life-cycle model, we attempt to find 2 It would also affect first time buyers. Whereas before the crisis, first time buyers only needed to save 5% of the value of the house, the required down-payments increased significantly after the crisis. 3

4 the main driving forces behind the difference in households consumption reactions over the crisis. In order to do so, we develop a dynamic structural model, which can be used for testing the existence of these different channels. 4

5 2 Consumption Growth and Leverage Aggregate consumption data from the Office of National Statistics (ONS) show that household spending was growing at an annual rate of 3.5% per year in the decade running up to the crisis before collapsing in 2008, remaining at below historical averages until recently (Figure 1). Figure 1: Annual growth in household spending Yet these aggregate data mask a large degree of heterogeneity across households. In Figure 2 we plot annual consumption growth for households with different housing tenures. Figure 2: Non-housing consumption growth The green line plots owner occupiers (with no mortgage debt); the yellow line plots households who have mortgage debt of less than twice their income; and the navy line plots households who have a high mortgage debt to income ratio of two or more. While 5

6 households across different types of home ownership reduced their consumption, the biggest adjustment came from those with a mortgage debt to income ratios above two. Our goal in this paper is to understand Figure 2 better, understand the mechanisms that lead high-leveraged households to cut their consumption by much more than lowleveraged ones. In this and the following section we focus on a deeper empirical analysis of the data available. 2.1 Data We use data from the Family Expenditure Survey (FES), a micro dataset containing detailed information on household expenditure of 5,000 to 6,000 households per year. A two-week expenditure diary accompanies the questionnaire. It therefore provides the best household-level consumption data in the United Kingdom. The FES also contains information on outstanding levels of mortgage debt from However, our main analysis predominantly covers the pre and post Great Recession period, i.e. from We focus on households of working age, where the head is aged between 21 and 69. Waves of the FES also switch between calendar and fiscal year collection multiple times, so to maintain consistency, we convert all data to calendar years. We use weekly non-housing expenditure as our measure of consumption because the methodology for calculating housing consumption in the FES is not consistent with that used in the National Accounts. For homeowners, the FES only measures mortgage payments rather than using a measure of imputed rents like that of the National Accounts. All data are deflated using the National Accounts consumption deflator. We focus only on secured debt as the FES has, at best, only scant data on unsecured debt. As secured debt accounts for the majority (80%) of all debt, we would not expect excluding unsecured debt to change the big picture results. The Survey contains no information on assets. To address this, we merge the FES with data from the Wealth and Assets Survey (WAS) at the cohort level. The WAS is a panel survey covering 20-30,000 households in each wave. The survey began in 2006 and has three waves available: Wave 1 from mid to mid-2008, Wave 2 from mid-2008 to mid-2010 and Wave 3 from mid-2010 to mid Specifically, we merge in mean values of real housing wealth and real gross non-housing financial wealth (excluding deposits). Unfortunately, the FES are an annual time-series of cross-sections, meaning we cannot control for individual-level heterogeneity or track changes over time. Instead, we 3 While the time periods from the WAS wave do not exactly match the calendar time periods in our analysis, they nonetheless provide a reasonable approximation, given that assets tend to change slowly. Using data from part of a WAS wave risks the data not being fully representative. 6

7 construct a synthetic panel, using date of birth, as first suggested in Deaton (1985b) and in line with what others using the FES have done in the past (see Attanasio and Weber (1994), Attanasio, Banks, and Tanner (2002), or Campbell and Cocco (2007) as examples). This method allows us to condition debt at its pre-crisis levels and to track changes in consumption over time, but it comes at the expense of reducing the degree of heterogeneity that are otherwise available at the household level. When converting data into a synthetic panel, there exists a trade-off between the number of cohorts and the number of data points to create each cohort observation. A greater number of cohorts increases the degree of heterogeneity within the dataset, but uses fewer data points to create each cohort observation, reducing the reliability of those estimates. Vice versa, fewer cohorts mean less variation between cohorts, but more reliable cohort level estimates. [do we need this paragraph?] Firstly, we pool two years together when defining pre and post crisis periods. We define as the pre-crisis period and as the post crisis year (we later extend the analysis to too). This pooling makes the time periods of the data more comparable to the WAS waves, where each wave also spans two years. It also allows us to increase the number of data points used to create each cohort level data point. Secondly, we use three different cohort definitions to ensure the reliability of our results. The first definition uses single birth-year cohorts. For example, everybody born in 1956 belongs to one cohort. Birth years are the cleanest definition of a cohort because it is a deterministic variable: people cannot move between different cohorts over time. However, they also combine people with and without mortgage debt making it harder to identify the relationship between debt and spending decisions. To discriminate between groups that do and do not have a mortgage, we consider a second cohort definition, splitting each birth year by mortgage status. The third definition also splits the sample by mortgage status but pools birth years into 5-year buckets. This definition allows the mean number of observations in each bucket to be larger than in the second definition - creating less volatility in the mean values - but it comes at the expense of having fewer observations in total. The main disadvantage of the second and third cohort definitions is that the sample is split by mortgage status, a choice variable (one decides whether or not to buy a house). The results may suffer from selection bias. We discuss our approach to dealing with this in Section??. 7

8 2.2 Descriptive Statistics The amount of debt a household have vary over their life-cycle. Households tend to accumulate debt when young converting them to assets as they age. Even so, there are changes over time and across different generations driven by factors such as rapid changes in house prices, the availability of cheap credit or macroeconomic factors, such as GDP growth. As levels of debt are negatively correlated with age, one might expect that younger households may be the predominant drivers of the navy line in Figure 2. For this reason, it is important to examine how debt, income and consumption have evolved over the life-cycle for different birth cohorts. Figure?? plots these three key variables of interest between (a) Real outstanding mortgage debt (b) Real weekly household income (c) Real weekly non-housing consumption Figure 3: Life-cycle behaviors of key variables by age across cohorts Each line represents a 10-year date of birth cohort, e.g. the pink line plots the cohort born between 1941 and One can see from Panel (a) that mortgage debt has been accumulating at a much faster rate than incomes for younger cohorts. Panel (b) shows that real incomes were growing at a much faster rate for younger groups in 8

9 the earlier years before starting to flat line. It is possible that the younger households were expecting their income to recover and grow at the same trajectory it did when they entered the workforce. If they were systematically over-estimating their income growth, then they may have also been comfortable taking on large levels of debt relative to their incomes. The financial liberalization of the 1990 s, which made credit more readily available, may have also played a role in the increase of debt among younger households. Panel (c) shows that consumption of younger groups has been growing much more slowly than for other groups before the crisis. This is unsurprising as incomes had also been slowing. The rapid accumulation of debt for younger generations has been predominantly driven by the increase in house prices relative to real incomes in the run up to the financial crisis. Panel (a) in Figure 4 shows that between 1995 and 2005, younger groups took the lion s share of this increase in debt. This stands in stark contrast to wealth accumulation (Panel (b)), where the biggest winners over the last decade have been the older generations. Panel (a) of Figure 4 also shows that the level of debt of younger groups has decreased since the crisis. This can be interpreted as evidence of younger households deleveraging. (a) Real outstanding mortgage debt (b) Real housing wealth Figure 4: Average household debt and housing wealth by age across years We report summary statistics from the FES and WAS in the Appendix. 3 A Simple Regression Analysis In this section, we are interested in exploring whether levels of leverage before the crisis are correlated with the weakness of consumption growth after the crisis. We are interested in two definitions of leverage: loan-to-income (LTI) and loan-to-value (LTV). 9

10 We specify 2006/07 as the period before the Great Recession and 2009/10 as the period after. Although we later also extend the analysis to 2011/12 to show that this effect is persistent. More specifically, we are interested in how households with leverage at different points in their life-cycle may have differentially affected consumption growth. 3.1 Baseline Estimations In our baseline estimation, we are interested in whether the level of loan-to-income (LTI) before the crisis (2006/07) had an effect on consumption growth after the crisis (2009/10). We estimate the following cross-sectional equation at the cohort level: c it = α 0 + α 1 LT I it 1 + α 2 y it + α 3 w it + α 4 x it + e it (1) Where c it is the change in log of non-housing consumption for cohort i, between , denoted by t, and the pre-crisis period, , denoted by (t 1). Our main variable of interest, LT I it 1, is the ratio of outstanding mortgage debt to net (post-tax) income in 2006/7, or the pre-crisis loan-to-income ratio. y it is the change in log net income; w it is a vector for the change in log of housing and financial wealth, taken from the WAS. The wealth variables allow us to control for developments on the asset side of the balance sheet. Finally, x it is a vector of additional controls, such as change in household composition. This equation is similar to Dynan (2012). Table 1 reports results from Equation 1. Each column represents one of the cohort definitions as specified in Section 2.1. Across all columns, the coefficients on the precrisis debt to income ratio are negative and statistically significant. They are also broadly similar in magnitude across all definitions. On average, we find that cohorts with a one unit higher LTI (e.g. 3 instead of 2) reduced their consumption by an extra % between 2006/7 and 2009/10. 4 The effect of increased leverage through LTI works not just via an increase in the numerator, but also through a fall in income. Households who were hit with a negative income shock would see an increase in their leverage, as measured by LTI. If the Great Recession was disproportionately unkind to younger households where they were more likely to become unemployed and experience bigger drops in their incomes then we would expect α 1 to be more negative for them. But leverage may also be affected by changes in house prices although those would only be indirectly captured by changes in loan-to-income ratios. A more direct way of 4 In most cases, the coefficients on the wealth variables are not clearly identified. That may be because the small sample sizes make it difficult to estimate these coefficient precisely. Nevertheless, these results are in line with some in the literature that show that changes in housing wealth do not determine household spending (Attanasio and Weber (1994)) 10

11 capturing how falls in house prices would affect leverage is through loan-to-values (LTV), the more commonly used definition of leverage. Cohort definition Single birth year Single birth year, 5 birth year, mortgagor mortgagor Dependent variable: C t [1] [2] [3] Y t 0.675*** 0.599*** 0.766*** (0.122) (0.118) (0.123) LT I t ** *** ** (0.014) (0.007) (0.009) Housing wealth t (0.070) (0.036) (0.059) F inancial wealth t *** (0.020) (0.023) (0.021) Constant ** ** (0.023) (0.012) (0.013) Controls Yes Yes Yes Observations Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1. Dependent variable is the change in log of non-housing consumption from 2006/07 to 2009/10. Y is the change in posttax income, net of mortgage interest payments between 2006/007 & 2009/10. Housing wealth and F inancial wealth are also for the same time period. LT I 06/07 is the ratio of outstanding mortgage debt to annual net income in 2006/07. Controls are the change in the number of adults and children between 2006/07 and 2009/10. Each column represents a synthetic panel regression from 2 pooled years, using one of four cohort definitions: using single birth years, single birth years, split by whether the household is a mortgagor or a non-mortgagor; 5-year birth buckets, split by mortgagor status and 10 year birth buckets, split by UK Government Office Region. Table 1: Baseline results (Loan-to-Income) Using the housing wealth data from WAS, we construct loan-to-values and estimate 11

12 the same equation as above but substituting LTIs with LTVs: c it = β 0 + β 1 LT V it 1 + β 2 y it + β 3 w it + β 4 x it + e it (2) This specification allows us to compare our results to other studies as the literature typically uses LTV as a measure of leverag, but it also serves as a useful cross-check to equation 1. The results are reported in Table 2. We find a statistically significant effect: for each 10% increase in LTV, consumption is reduced by % between 2006/7 and 2009/10. A fall in house prices would increase LTVs making it harder (or more expensive) to refinance. It also makes it harder to move on to or up the housing ladder, as it would require saving for a bigger deposit. If younger households are more highly leveraged (i.e. have larger loans) compared to households of an older generation (because of the rapid rise in house prices), then a fall in house prices would increase LTVs for those younger households by more than older, less-leveraged households. If, after the crisis, the availability of credit requires achieving higher credit scores than what was acceptable before the crisis then we would expect a more negative β 1 coefficient for younger households, who because of their shorter financial histories have weaker credit scores. To simplify matters we use only one cohort definition for the remainder of the analysis. We prefer to use single birth years split by mortgagor status for three reasons. One, given that we are analyzing the effect of household debt on spending, it makes sense to have a pseudo panel that groups households by mortgagor/non-mortgagor status. Second, the coefficient sizes for pre-crisis LTI and LTV using that definition falls in between the other two cohort definitions. Third, this definition yields the largest number of observations, which will come in quite handy when we split the sample by age. The main criticism of using this cohort definition is that mortgagor status is a choice variable, so the construction of the panel does not just rely on deterministic variables. Following Attanasio, Banks, and Tanner (2002), we use predicted mortgagor status (instead of actual status) to construct the an alternative panel specification 5. We get the same results using predicted variables as we would actual variables. The detailed method and results are discussed in Appendix A We also use predicted debt for the LTI ratio. 12

13 Cohort definition Single birth year Single birth year, 5 birth year mortgagor mortgagor Dependent variable: C t [1] [2] [3] Y t 0.743*** 0.607*** 0.857*** (0.124) (0.117) (0.130) LT V t * *** ** (0.064) (0.038) (0.054) Housing wealth t (0.096) (0.036) (0.061) F inancial wealth t *** (0.020) (0.023) (0.021) Constant ** ** (0.029) (0.012) (0.013) Controls Yes Yes Yes Observations Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1. Dependent variable is the change in log of non-housing consumption from 2006/07 to 2009/10. Y is the change in post-tax income, net of mortgage interest payments between 2006/007 & 2009/10. Housing wealth and F inancial wealth are also for the same time period. LT V 06/07 is the ratio of outstanding mortgage debt to housing wealth in 2006/07. Controls are the change in the number of adults and children between 2006/07 and 2009/10. Each column represents a synthetic panel regression from one of four cohort definitions: using single birth years, single birth years, split by whether the household is a mortgagor or a non-mortgagor; 5-year birth buckets, split by mortgagor status and 10 year birth buckets, split by UK Government Office Region. Table 2: Baseline results (Loan-to-Value) 3.2 Effect by age Household debt accumulation is disproportionately skewed towards younger households, paying it down as they grow older. But there is also evidence to suggest that the Great 13

14 Recession was harsher for younger households than older household: they had bigger falls in their income and more were more likely to become unemployed. It may also be that they experienced tighter conditions accessing credit than older households. Sample split: Young Old Dependent variable: C t [1] [2] [3] [4] Y t *** 0.708*** (0.302) (0.317) (0.133) (0.134) LT I t *** ** (0.012) (0.008) LT V t *** ** (0.054) (0.045) Housing wealth t 0.097* 0.101* (0.044) (0.047) (0.063) (0.062) F inancial wealth t (0.039) (0.041) (0.025) (0.025) Constant ** ** (0.065) (0.069) (0.014) (0.014) Controls Yes Yes Yes Yes Observations Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1. TBD Table 3: Age split To check if there was a differential effect on consumption between young and old households, we split the sample by age those who are older than 35 and those 35 years or less. The results, reported in Table 3, indicate that the biggest cuts to consumption were driven by the younger households the coefficients on LT I t 1 and LT V t 1 are about three times larger for younger than for older households. 3.3 Robustness We test out different specifications to check the robustness of our results. We summarize those below, but details of all robustness tests can be found in the Appendix??. First, 14

15 we show that defining cohorts using mortgagor status is not particularly problematic. Over long periods of time, households will move between different housing tenures. Data from the WAS suggest that around 90% of the households who had a mortgage in the first wave of the survey, between mid-2006 and mid-2008, still had a mortgage two years later. We can therefore assume that over shorter periods - such as when looking at changes over the financial crisis period - mortgage level is fixed. Nevertheless, we cross-check our results by also using predicted, rather than actual, mortgagor status, as suggested by Moffitt (1993). We get the same results. Second, we extend the time period to 2011/2012 to check for persistence. We find that extending out estimation period does little to change the size and significance of the LTI and LTV coefficients, suggesting that the larger cuts in spending by leveraged households had not dissipated, at least up to Third, we test for non-linearities in leverage by checking whether households with higher loan-to-incomes cut their spending by more than those with lower values. We find that households who have an LTI of greater than 4 or more cut their consumption by 41% more than households who had an LTI of 4 or less. These effects are also persistent: we find a similar coefficient if the analysis is extended to 2011/12. The final check we do is test for spuriousness of our results. We do this by running placebo regressions for two alternative time periods, in place of the pre-crisis base year of 2006/07. The first time period we use is between and ; and the second time period is between and We find no effect using those two alternative time-periods: the coefficients are very small and statistically insignificant. 4 Life-Cycle Model with Mortgages In a regression analysis it is impossible to disentangle how consumption cuts of high and low- leveraged households were affected by different shocks around the recession. We can not test wether the empirical connection between the size of the consumption cut and the leverage can be better understood with income shocks, credit market shocks or house price shocks. For this reason, in this section we build a theoretical model and simulate the behavior of a large number of households. In this way we are able to analyze counterfactuals and identify the most likely recession scenarios. We start with a simple model of life-cycle consumption and savings in a dynamic stochastic framework. Households maximize their present discounted lifetime utility, which depends on nondurable consumption and the consumption of a flow of housing services. They can move resources between periods by investing in either a fully liquid asset equivalent to a one-period bond or less liquid housing, which also provides a flow 15

16 of housing services. We only allow households to have collateralized debt, where housing could serve as collateral. Households face uncertainty in two dimensions: idiosyncratic uncertainty over labor income and aggregate uncertainty over the house price. We do not consider bequest motives and an uncertain end of life. 4.1 Model structure The problem of the households can be written as subject to V t (Ω t ) = max U(C t, S t ) + βe t V t+1 (Ω t+1 ) (3) {C t,i t,ξ t,ϑ t} X t+1 = R X (X t C t Q t I t Θ t ξ t + ϑ t ) + Y t+1 (4) Households get utility from nondurable consumption, C t and housing services, S t. Ω t is the vector of state variables, Ω t = (X t, H t, M t, Q t, Yt P ). Households start any period t with a given amount of wealth and receive uncertain labor income, Y t, that add up to cash-on-hand, X t. Given the amount of cash-on-hand, households decide how much to consume, C t, how much to invest in an illiquid housing, I t at unit price Q t, how much repayment to make on the existing mortgage, ξ t and how much new mortgage to take out, ϑ t. Depending on the size of housing adjustment, households have to pay a cost, Θ t. Yt P denotes permanent income, which we discuss later. Utility function. We use a CRRA utility function in the composite good. Nondurable consumption and housing services are aggregated with a Cobb-Douglas technology into the composite good. u(c t, S t ) = ( ) C α t St 1 α 1 ρ 1 ρ where α is the weight on nondurable consumption in the utility function, ρ is the inverse of the elasticity of intertemporal substitution (for the composite good). Housing. Housing investment, I t, adds to the existing housing, H t. Hence the law of motion for the housing is (5) H t+1 = H t + I t, H 0 > 0 (6) The purchase of housing may often be associated with significant cost such as time spent looking for the preferred house or contractual costs. To capture such types of costs, we allow for non-convex adjustment costs Θ(I t ) 0, which we assume to depend on the 16

17 value of housing investment Θ(I t ) = δq t I t (7) Housing generates housing services, S t. We assume a linear technology between housing and housing services. Since there is no rental market in our model housing services are only acquired by owning. S t = bh t (8) Housing can be used as collateral for mortgage loans. Households can get collateralized debt at a constant price of R M up to a given fraction, 1 ψ, of the value of housing. At the moment of the first mortgage take-out, the following inequality has to hold M t (1 ψ)q t H t (9) where ψ can be interpreted as the down-payment requirement. Financial markets. We only allow households to have collateralized debt. Other types of debt are not available. This is not an unreasonable assumption as mortgages constitute the vast majority of loans in the household sector in the UK. Consequently this means that households have an incentive to take out a mortgage even if the mortgage rate is higher than the risk-free rate. Households with an existing mortgage, M t can apply for a new mortgage, ϑ t, although they have to keep repaying the existing mortgage, ξ t. The law of motion for the mortgage stock is as follows M t+1 = R M M t + ϑ t ξ t (10) Next period s mortgage equals the existing mortgage with its interest, R M, 6 plus the new mortgage taken out minus the repayment on the existing mortgage. We assume that repayment on the existing mortgage is bounded from below. Households have to pay at least the interest on the value of the mortgage in each period. Also there is a natural upper bound for repayment, which is paying back all the mortgage with all its interest. r M M t ξ t R M M t (11) As highlighted earlier, households are assumed to face a constraint on the level of mortgage they can take out. The maximum amount of mortgage they can have is a constant 6 R M is the gross real mortgage rate, R M = 1 + r M 17

18 fraction of the value of their housing. { (1 ψ)q t H t R M M t if (1 ψ)q t H t > R M M t ϑ t = 0 else (12) It is important to see from equation (12), that the restriction on the mortgage relative to the value of housing is only enforced at the moment of taking out new mortgage. As house prices do fluctuate, the constraint can be violated for households with an existing mortgage as there is no mechanism through which households could insure themselves against this uncertainty. In this manner, whenever the existing mortgage exceeds the maximum possible mortgage take-out, households can not apply for a new mortgage. Whenever households borrow they are also subject to the terminal condition, M T = 0, which prevents them from borrowing more than they can repay with certainty by the end of their life. Uncertainty. In our baseline model households face uncertainty in two dimensions: idiosyncratic uncertainty over labor income and aggregate uncertainty over house prices. Following Zeldes (1989), labor income Y t at any time before retirement is exogenously described by a combination of deterministic and random components Y t = Y P t Z t log(z t ) N( 0.5σ 2 z, σ 2 z) (13) where Yt P is the permanent component and Z t is the transitory component. Furthermore we assume that the permanent component can be described as Y P t = G t Y P t 1N t log(n t ) N( 0.5σ 2 n, σ 2 n) (14) with G t being a deterministic function of age and N t is the innovation. We also assume that the shocks (N t and Z t ) are independent. Labour income Y t at any time after retirement is a constant fraction a of the last working year s permanent labor income. Y t = ayw P (15) The log of the house price is assumed to be determined by a random walk process with drift. In Section 4.3 we show that this assumption is consistent with the UK house price data. log Q t+1 = d 0 + log Q t + log ε t log(ε t ) N( 0.5σε, 2 σε) 2 (16) It is important to highlight that the log-normality assumption about the idiosyncratic shocks to labour income, Z t and N t, and about the aggregate shocks to house prices, ε t, 18

19 is only relevant in our baseline specification. When we 4.2 Solution and Simulation The life-cycle problem can not be solved analytically, we therefore apply numerical techniques. Given the finite nature of the problem, a solution exists and can be obtained by approximating optimal policy functions with backward induction technique. We use the backward induction over the normalized value function of the households to obtain the optimal policy functions. Expectations in the model refer to uncertain incomes and house prices, while they are evaluated by using the Gauss-Hermite approximation. Since shocks to incomes and prices, Z t+1, N t+1 and ε t+1 are log-normally distributed random variables in each period, we are able to use a three-dimensional Gauss-Hermite quadrature to approximate the expectations as follows E t V t+1 (ω t+1 ) = = 1 π V t+1 1 i j π wgh i k ) V t+1 (ω t+1 (Z, N, ε) df (Z)dF (N)dF (ε) ( ω t+1 ( 2σ Z Z, 2σ N N, ) 2σ ε ε) e (Z2 +N 2 +ε 2 ) ( wj GH wk GH V t+1 ω t+1 ( 2σ Z Z GH where ω t+1 is the vector of normalized state variables, Z GH i Gauss-Hermite nodes and wi GH, wj GH and wk GH backward induction, we get the optimal policy functions. i, 2σ N Nj GH, ) 2σ ε ε GH k ) (17) s, Nj GH s and ε GH k s are the are the corresponding weights. Using Having the optimal policy functions calculated, we simulate the behavior of households over the life-cycle. For each simulation we draw realizations for the two individual shocks, the permanent income shock and the transitory income shock and realizations for the aggregate house price shocks which are identical for all the households. As we disregard from any kind of bequest motive households start their life with zero wealth, and they get labor income. 4.3 Model Calibration Most of the parameter values for the life-cycle model presented above are adapted from the existing literature. Here we only discuss the values of parameters, which we estimate from different data sources. Income process. To obtain the age-specific component of the life-cycle income profiles (G), we fit a second-order age polynomial to the logarithm of cohort income data 19

20 gathered from the Family Expenditure Survey between 1996 and ln y c t = γ 0 + γ 1 age c,t + γ 2 age 2 c,t 10 (18) where c refers to cohort averages. The regression results are presented in Table 4. Age Age 2 Constant log y c (0.003) (0.000) (0.058) Observations 945 R-squared Standard errors are in parenthesis. *** p < 0.01, ** p < 0.05, * p < 0.1 Table 4: INCOME PROCESS House price process. We estimate the house price process based on Nationwide s House Price Index adjusted for retail prices (using the Office for National Statistics Retail Price Index) for quarters 1996q1-2015q2. We estimate an AR(1) process with linear trend for the logarithm of the real house price index. log Q t+1 = q 0 + q 1 t + ρ h log Q t + log ε t (19) The result of the estimation is in Table 5. The persistence parameter ρ h of the log real house price is estimated to be very close to one and the unit root tests do not reject the null hypothesis that this parameter is actually 1. It implies that the log real house price process can be approximated by a random walk. The estimated quarterly variance of the house price shock, σε, 2 equals , which corresponds to at an annual frequency. The benchmark model parameters are collected in Table 6. Cohorts. We define different groups of households, and simulate their behaviour separately, taking into account that different cohorts experience aggregate shocks at different ages. Altogether we define 6 cohorts between ages 20 and 80 (10-year age interval each) and simulate 1000 households in each cohort. 20

21 log Q t (0.0000) log Q (-1) (0.012) constrained Constant (0.137) (0.002) σε Observations R-squared Standard errors are in parenthesis. *** p < 0.01, ** p < 0.05, * p < 0.1 Table 5: HOUSE PRICE PROCESS Parameter Value Source T Number of years as adult 60 W Number of years as worker 45 β Discount factor 0.95 ρ Risk aversion parameter 1.5 Blundell, Browning, and Meghir (1994) Constant Age-specific income, constant Own calculations, FES Age Age-specific income, linear trend Own calculations, FES Age 2 /10 Age-specific income, quadratic trend Own calculations, FES a Replacement rate 0.72 Own calculations, FES σ n Std.dev.permanent income shock Carroll and Samwick (1997) σ z Std.dev.transitory income shock 0.21 Carroll and Samwick (1997) σ ε Std.dev.house price shock Own calculation, Nationwide ρ h Persistence parameter for house price 1 Own calculation, Nationwide R X Liquid asset return 1.02 Gourinchas and Parker (2002) R M Mortgage rate 1.03 α Weight of durables in composite good 0.83? b Housing service technology 0.06? δ Adjustment cost 0.05 ψ Down-payment requirement 0.2 Table 6: PARAMETERS FOR THE BENCHMARK MODEL 21

22 5 Simulation Results In this section we present results from the numerical simulation. Similarly to the empirical part, in the simulation we define two groups of households: high-leveraged and low-leveraged households. Households with mortgage-to-income ratio above 2.5 are defined as high-leveraged households, while households with mortgage-to-income ratio below 2.5 as low-leveraged households. We present our results separately for high- and low-leveraged households. First, in our baseline simulation, we disregard of the 2008/2009 recession. Then, we extend our analysis and model the recession in four different ways. Our aim with this exercisse is to identify the main driving forces behind our empirical observation discussed in Section 2: high-leveraged households cut their consumption by much more than low-leveraged households in response to the crisis. Following Alan, Crossley, and Low (2012) we consider four different sources of the 2008/2009 recession: negative shock to income, increased uncertainty around future income, reduction in the credit supply and fall in house prices (i.e. reduction in housing wealth). 5.1 Baseline In our baseline specification we analyse the model without considering the recession in It means that we do not take into account big house price or income shocks around Therefore, we simulate households according to the model described in the previous section. Figure 5 shows the simulated level of the average consumption between 1992 and Even though the average consumption is calculated over all the cohorts, there is a steady increase in consumption over the observed period. This moderate increase in average consumption can be rationalized by the model assumption in equation (16): the level of house prices are increasing over time only with small disturbances around its trend. This leads to a constant increase in housing wealth, therefore a constant increase in consumption. The vertical black line corresponds to year

23 Baseline year Figure 5: LEVEL OF CONSUMPTION In Figure 6 we disaggregate the simulated consumption data by cohorts and by the level of indebtedness. First, we define two broad groups: households in the three youngest cohorts out of the six cohorts are labelled as young, while the rest of the households are labelled as old. As it is visible from Figure 6 young households experience a sharp increase in their consumption between 1992 and Moreover, the increase is much sharper than the one for the aggregate consumption shown in Figure 5. The reason behind is that young households are liquidity constrained: at the beginning of their life-cycle they adjust their consumption to their quickly increasing income. The consumption of old households are steady over the same period. Second, we categorize households into two different groups by a leverage criteria: households whose mortgage-to-income ratio is below 2.5 at year 2007 are labelled as low-leveraged households, while the ones above the 2.5 threshold are labelled as highleveraged households. 23

24 year year Young Old High Leverage Low Leverage Figure 6: LEVEL OF CONSUMPTION FOR DIFFERENT GROUPS High-leveraged households only have slightly lower levels of consumption in 1992 than low-leveraged ones, while this gap is broadening over the observed time period. Therefore, on average high-leveraged households have lower consumption over their lifecycle. Figure 7 similarly to Figure 2 shows the year-to-year consumption growth separately for households with high- and with low leverages for the period of Consumption growth of households with high leverages are in general lower than that of households with low leverages. The only exception is around 2009/2010. Recall that in our baseline model specification there is no mechanism to generate the 2008 recession. Hence, it is just a coincidence that the time series for high-leveraged households deviates from its trend exactly around the the years associated with the great recession in the real world. 24

25 Baseline year High Leverage Low Leverage Figure 7: NO RECESSION CONSUMPTION GROWTH 5.2 Different Models of Recession In this part of the paper we analyse different models of recession and discuss wether they could explain the empirical fact that high-leveraged households have cut their consumption by more than low-leveraged ones in the 2008 recession. In the following, we consider four alternative shocks that could have caused the 2008 recession, or what households may have thought of what has happened. Permanent Income. A recession may occur when all the households face a negative income shock at the same time. We model this scenario by assuming that the expected value of the permanent income shock, N t, decreases from 1 to 0.8 for one period in More precisely, N 2008 = 0.8N 2007 for each household and the rest of the shocks are drawn from the same lognormal distribution we have introduced in Section 4.1, log(n t ) N( 0.5σ 2 n, σ 2 n). Variance of the Permanent Income. The other alternative cause of recession is that from 2008 onwards households experience a higher level of uncertainty about their future labor income. We simulate this situation by considering an increase in the variance of 25

26 the permanent shocks to income. log(n t ) N( 0.5σ 2 n, σ 2 n) if t < 2008 log(n t ) N( σ 2 n, 2σ 2 n) if t 2008 Note that in order to keep the expected value of the shock fixed, E(N t ) = 1, doubling the variance of the lognormal distribution needs doubling the mean of it as well. Downpayment Requirement. We can think of the recession as a period with decreased supply of credit. In fact, banks changed their credit conditions dramatically after 2008 and most importantly they increased their downpayment requirements. Instead of, on average, 10% down-payment they have started to demand around 20% down-payment. In our model down-payment requirement is led by a single parameter, ψ, as seen in equation (9). Hence in our simulations we set: ψ = 0.1 if t < 2008 ψ = 0.2 if t 2008 House Prices. The last alternative we consider is the collapse of the house prices after Instead of the estimated house price process in Table 5, we feed the model with the observed house price data. 7 After simulating these alternative scenarios, we are able to compare the effect of different types of shocks to the baseline, no recession scenario. We are concerned about consumption growth, therefore we calculate how the consumption growth of different models deviates from the no recession case. In Figure 8 we present the results for all the simulated households in the sample - aged 20 to 80. We again separate high and low-leveraged households according to the 2.5 mortgage-to-income-ratio criteria. The numbers of the y-axises should be interpreted as percentage points deviations in consumption growth from the no recession case. Four facts are worth noticing here. First, only permanent income drop and the increase in the down-payment requirement can lead to a sudden drop in consumption in Second, both of these shocks generate higher consumption cuts for highly indebted households, which is consistent with our empirical observation. Third, the increase in the variance of the permanent income shock only has long-term effects. As we can see in Figure 8, both the high- and low-leveraged households decrease their consumption persistently after And fourth, house price evolution can not account for the immediate cut of 7 See the graph of observed house prices in the UK in the Appendix 26

27 consumption in WHY???!!!! Permanent Income Drop Increase in Permanent Income Variance year year Increase in Downpayment Requirement Observed House Price year year High Leverage Low Leverage Figure 8: DEVIATION IN CONSUMPTION GROWTH FROM NO RECESSION 5.3 Young versus Middle-Aged In the previous section we have identified two types of shocks that could generate differences in consumption cuts between low- and high-leveraged households: the permanent income shock and the shock to the credit supply. In this section we investigate the effects of these two shocks further by disaggregating the simulated data. As, by assumption, permanent income shocks do not affect retired households, we only focus on households between age 20 and 60 (4 simulated cohorts) in each scenarios. We define two groups: households between 20 and 40 years of age are selected into the group of young households, while households between ages 40 and 60 into the group of middle-aged households. In Figure 9 we show consumption growth over time under the scenario, when the recession is interpreted as a sudden drop in the permanent income of households. Both young and middle age households experience a sudden drop in consumption in 2008, while there is a significant difference between consumption cuts of high- and low-leveraged households for each age group. Middle-aged households make bigger adjustments to their 27